Event-based control has received considerable attention due to its irreplaceable advantage in resource limited systems. In this paper, event-based consensus of second-order discrete-time multi-agent systems is investigated. The event-based controller is designed for each agent, which is based on the state measurement error among neighborhood agents. at its own triggering time instants. Some sufficient conditions are obtained for achieving consensus. To avoid observing the current states of its neighbor agents as well as its own state at every discrete-time, a self-triggered approach is presented to determine the triggering time sequence. Furthermore, certain conditions are given to avoid controller update at every discrete time. Finally, a simulation example is given to illustrate the efficiency of the proposed control strategy. (C) 2017 Elsevier Ltd. All rights reserved.